Somebody said -

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

==============================

No problem !

The fixed standard arm of the rho bridge (instead of a 50-ohms resistor) can
be just a very long length of transmission line of input impedance Zo =
Ro+jXo which, of course, varies with frequency in exactly the required
manner.

Or, as I often did 50 years back, make an artificial lumped-LCR line
simulating network to any required degree of accuracy.
----
Reg

"Dr. Slick" wrote:

wrote in message ...

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

It is not nearly that tricky. 'Revised' rho, as you state,
predicts 0 Volts across the capacitor. This will be easy to
measure with any AC voltmeter that can handle your test frequency.

Perhaps, but i'm interested in the forward and reflected
waves, which you can only get with directional couplers on a line of
the same Z as the Zo, i suspect. So even if you get 0 volts, there
are still fwd and rev waves.

But what if you do not get zero volts. Sort of messes up the
'revised' rho theory a bit, does it not?

I predict, using circuit theory, that if you excite the
test circuit with a 1 Volt sinusoid at a frequency that
makes the impedances j200 and -j200, that you will measure
4 Volts across the capacitor, not 0. This aligns with the
result expected from 'classic' rho.

Go ahead and bench test it, and let us know what you find.

Rummage. Rummage. Rummage.
2.2 uH +/- 10%, 100 pf tolerance unknown, 33 ohms +/- 5%

R = 34 measured
L = 2.2 uH
C = 100 pF
But wait, there will be a scope probe across C, vendor says
15 pF nominal when compenstaed for a 15 pF scope input, but
the scope input is 20 pF. Oh well, use 15 pF anyway. So:
C = 115 pF

f = 10.006 MHz
Zres = 34 + j0
Zind = 0 + j138.3
Zcap = 0 - j138.3

But it is always wise to predict the outcome before the measurements...

So let's use a 1 Volt sinusoid at 10.006 MHz.

From circuit theory:
Ires = 0.02941 + j0 A
Vcap = 4.067 /_ -90 V

From 'classic' rho:
Vi = 0.5 V
rho = (Zl-Z0)/(Zl+Z0)
= ((0 -j138.3)-(34+j138.3))/((0 -j138.3)+(34+j138.3))
= 8.1965/_ -97.0
Vr = Vi * rho
= 0.5 * 8.1965/_ -97.0
= 4.09826/_ -97.0 V
Vcap = Vload = Vi + Vr
= 0.5 + 4.09826/_ -97.0
= 4.067/_ 90.0 V

So I expect the magnitude of the voltage to be 4.067 volts.

But wait, there are a whole bunch of tolerances so that is
unlikely to be the voltage, so what is the expected range?

We are not sure of the capacitor tolerance but it is unlikely
to be better than 10% and the scope probe is unknown, so let's
call it 10%.
The resistor was measured at 34 +/- 1 digit + meter error, so
5% is probably good.

So if the capacitor is 10% high and resistor is 5% low the
error would be 1.1/.95 = 1.16 or about 16%. So if the
result is within 16% of 4.067 it will be consistent with
expectations.

First adjust frequency for resonance
f = 10.14 MHz, tolerably close to the predicted 10.006 MHz.

And the measured voltage across the capacitor is...

Hold on, before revealing the answer....

In the interests of minimizing the wiggle room, perhaps you
would be so kind as to provide your prediction for the voltage
across the capacitor. Using 'revised' rho, in a previous post
I recall you predicted 0 volts. Is this still your expectation?

....Keith

David Robbins wrote:

wrote in message ...
"Dr. Slick" wrote:

wrote in message
...

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

It is not nearly that tricky. 'Revised' rho, as you state,
predicts 0 Volts across the capacitor. This will be easy to
measure with any AC voltmeter that can handle your test frequency.

Perhaps, but i'm interested in the forward and reflected
waves, which you can only get with directional couplers on a line of
the same Z as the Zo, i suspect. So even if you get 0 volts, there
are still fwd and rev waves.

But what if you do not get zero volts. Sort of messes up the
'revised' rho theory a bit, does it not?

the 'revised' rho predicts zero reflect 'power waves' as defined by
kurokawa... it says nothing about voltage or current waves.

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

This could work, I supposed, but this discussion started with an
assertion that 'classic' rho was WRONG because it resulted in
more reflected power than incident. My contention is that
'classic' rho is correct and yields the correct voltages regardless
of the results obtained when |rho|^2 is used to predict powers.

If kurokawa wishes to introduce a new rho to solve these problems
in a different manner, that is fine, but he would have reduced
confusion significantly if he had not called it rho.

....Keith

And that's the whole crux of the problem -- the mistaken assumption that
the "reflected power" can never exceed the "forward power". Once you
accept that erroneous idea as a fact, you're stuck with some very
problematic dilemmas that no amount of fancy pseudo-math and alternate
reflection coefficient equations can extract you from. A very simple
derivation, posted here and never rationally disputed, clearly shows
that the total average power consists of "forward power" (computed from
Vf and If), "reflected power" (computed from Vr and Ir), and another
average power term (from Vf * Ir and Vr * If) whenever Z0 is complex.
The only solid and inflexible rule is that these three always have to
add up to the total average power. Not that the "forward power" always
has to equal or exceed the "reflected power". It's in that false
assumption that the problem lies.

Roy Lewallen, W7EL

wrote:

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

This could work, I supposed, but this discussion started with an
assertion that 'classic' rho was WRONG because it resulted in
more reflected power than incident. My contention is that
'classic' rho is correct and yields the correct voltages regardless
of the results obtained when |rho|^2 is used to predict powers.

If kurokawa wishes to introduce a new rho to solve these problems
in a different manner, that is fine, but he would have reduced
confusion significantly if he had not called it rho.

...Keith

wrote in message ...
David Robbins wrote:

wrote in message
...
"Dr. Slick" wrote:

wrote in message
...

The tricky part is measuring this correctly, because you
would need an SWR meter that is calibrated for the same Z as
Zo.

It is not nearly that tricky. 'Revised' rho, as you state,
predicts 0 Volts across the capacitor. This will be easy to
measure with any AC voltmeter that can handle your test frequency.

Perhaps, but i'm interested in the forward and reflected
waves, which you can only get with directional couplers on a line of
the same Z as the Zo, i suspect. So even if you get 0 volts, there
are still fwd and rev waves.

But what if you do not get zero volts. Sort of messes up the
'revised' rho theory a bit, does it not?

the 'revised' rho predicts zero reflect 'power waves' as defined by
kurokawa... it says nothing about voltage or current waves.

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

even worse... the 'new' one is based on kurokawa's specific definition of a
'power wave'. this 'power wave' is obviously defined to avoid some of the
discussion we have been having when talking about forward and reflected
powers, but it is not 'power' as discussed in most other places. it is
instead a contrived wave formula specifically chosen to make power
calculations easier as kurokawa states just before defining the forward and
reflected 'power waves' as:

a=(V+ZI)/2sqrt(|ReZ|) and
b=(V+Z*I)/2sqrt(|ReZ|)
(subscripts 'i' left off all terms for readability)

these definitions of course make it harder to calculate the underlying volta
ges and currents, but make it easy to calculate power and power reflections
from a multi port network as you simply define the 'power wave reflection
coeficient' as s=b/a and the 'power reflection coefficient' as |s|^2. note,
at no point does kurokawa use rho. In one point just after defining s (eqn
11) and expanding it by substitution to s=(Zl-Zo*)/(Zl+Zo) (eqn 12) and
further into R,X terms (eqn 13) it is compared to the significance of the
'conventional voltage reflection coefficient', there is no mention that this
should replace the 'conventional' rho, nor that it should give the same
results.

i think the more important thing now is to point out to the arrl the error
of using that form of the reflection coefficient in place of the
'conventional' one in the latest antenna book so it doesn't become gospel in
the future.

Reg:

[snip]
The fixed standard arm of the rho bridge (instead of a 50-ohms resistor)
can
be just a very long length of transmission line of input impedance Zo =
Ro+jXo which, of course, varies with frequency in exactly the required
manner.

Or, as I often did 50 years back, make an artificial lumped-LCR line
simulating network to any required degree of accuracy.
----
Reg
[snip]

Caution... take care, the "reflection police" may get ya!

Roy and Dave took me to task on another thread for even suggesting just such
an
approach. A semi-infinite line!!! Hmph... no way they were gonna let me
get away
with that. Roy wanted to know what "semi-infinite" was!!!

Dave even told me that my idea of having a lumped approximation to Zo was
impossible!
This was a completd surprise to me since over 300,000 units of an xDSL
transceiver I
recently designed for the commercial marketplace and which have all been
shipped
and installed by BellSouth, Verizon, SBC and other such unknowing folks
incorporates
just exactly that kind of circuitre!

Hmmmm... I guess I lucked out and none of those customers noticed I was
balancing \
a lumped approximation of Zo against a real distributed complex Zo!

:-)

--
Peter K1PO
Indialantic By-the-Sea, FL.

Chipman, page 138, presents an equation for the power at any point 'z' on a
line that involves Zo and considers the case where Zo = Ro+jXo. He then
derives two equations: one for the real component of the power Pr measured
at any point 'z' on a line and another for the imaginary component of power
Pi at that point. Watts and VARs . . .

Each equation contains three terms. The second equation for Pi and the third
term in both equations vanish when the value of Xo is zero. The condition
that the real part never be negative is shown to be that Xo/R0 is equal to
or less than unity.

He first, however, derives the reflection coefficient for the point 'z'
which is stated as p(z) = (Z(z) - Zo)/(Z(z) + Zo) and Zo is defined to be a
complex number. Some authors have referred to this as "Classical Rho."

Chipman's interpretation of this equation for Pr of three terms is that the
first term represents the real power for the incident wave alone at a point
'z'; the second term relates to the real power in the reflected wave at that
same point; and the third term (which vanishes for real Zo) represents "an
interaction between the reflected and incident waves." This is in effect the
third term that Roy obtained using Vf * Ir and Vr * If.

Thus on a line with real Zo, the net average power in the load is always
given by Pf - Pr. However, with lossy lines having Xo not equal to zero, all
three terms of the equation must be taken into account in determining the
net power at any point along the line. And thus, Pr and Pf alone do not
describe the load power.

He further states that passive terminations exist which can result in
classical rho achieving a value of 2.41 "without there being any implication
that the power level of the reflected wave is greater than that of the
incident wave." The physical example is that of the resonance obtained by
conjugate matching of the Xo-component of the line with the load and the
attendant "resonant rise in voltage.".

The existence of this third term is, I believe, what much of the discussion
has talked around and attempted to avoid confronting by involving all manner
of arcane definitions and interpretations to "prove" that the net power
delivered to a load cannot be other than Pf-Pr and that Pf is always larger
than Pr.

Note that this work is not mine - I am merely reporting the gist of
Chipman's derivations and interpretations due to the scarcity of his book.

This plus Roy's presentation is enough for me . . .

--
73/72, George
Amateur Radio W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13QE
"Starting the 58th year and it just keeps getting better!"






"Roy Lewallen" wrote in message
...
And that's the whole crux of the problem -- the mistaken assumption that
the "reflected power" can never exceed the "forward power". Once you
accept that erroneous idea as a fact, you're stuck with some very
problematic dilemmas that no amount of fancy pseudo-math and alternate
reflection coefficient equations can extract you from. A very simple
derivation, posted here and never rationally disputed, clearly shows
that the total average power consists of "forward power" (computed from
Vf and If), "reflected power" (computed from Vr and Ir), and another
average power term (from Vf * Ir and Vr * If) whenever Z0 is complex.
The only solid and inflexible rule is that these three always have to
add up to the total average power. Not that the "forward power" always
has to equal or exceed the "reflected power". It's in that false
assumption that the problem lies.

Roy Lewallen, W7EL

wrote:

So is kurokawa proposing two completely different rhos?
One for computing voltages and currents and the other for power?

This could work, I supposed, but this discussion started with an
assertion that 'classic' rho was WRONG because it resulted in
more reflected power than incident. My contention is that
'classic' rho is correct and yields the correct voltages regardless
of the results obtained when |rho|^2 is used to predict powers.

If kurokawa wishes to introduce a new rho to solve these problems
in a different manner, that is fine, but he would have reduced
confusion significantly if he had not called it rho.

...Keith

| George, W5YR wrote:
| ...
| The condition
| that the real part never be negative
| is shown to be
| that Xo/R0 is equal to
| or less than unity.
| ...

Unfortunately,
I am afraid this is
_not_
the case at all.

Exactly, the related lines have as follows:

"The condition that Pr should never become negative is that
|p(z)|^2 + 2(Xo/Ro) Im p(z) = 1
Expanding p(z) from (7.33) with Zo = Ro + jXo and Z(z) = R(z) + jX(z),
it is easily found that this reduces to the condition |Xo/Ro| =1,
which has already been seen to be true."

Mrs. yin,SV7DMC, who has repeated, checked and solved
all of this book materials, except perhaps a few,
forewarns of that:
Every time Chipman says "easily", probably implies
"as I heard or read or something like that".
How else can someone explains,
why the proof of every such claim by him,
it happens to be a so cumbersome one?

This is true especially this time.

If someone follows the Chipman's hint,
the equivalent condition at which "easily" arrives
is only Z(z) = 0.
[e.g. in the thread
'Complex Z0 - Power : A Proof' - The Missing Step]


After that,
this last condition is unquestionably valid at the terminal load,
when we impose Z(l) = Zt = Rt +jXt, with Rt = 0.

At every other point it is still an unproven, open, problem,
at least to me.

But there is a chance to finish with this matter...

According to Mr. Tarmo Tammaru/WB2TT
in the thread 'Complex line Z0: A numerical example':

"I did a search, and came up with a Robert A Chipman, age 91, in Toledo OH.
From my recollection, the age is about right, and Toledo is where I saw him"


Therefore,
I think it is the most appropriate time,
someone curious enough of you,
who leaves somewhere near by him,
to go and ask him about it.

Is there any volunteer?

Sincerely,

pez
SV7BAX

"David Robbins" wrote in message
...

i think the more important thing now is to point out to the arrl the error
of using that form of the reflection coefficient in place of the
'conventional' one in the latest antenna book so it doesn't become gospel
in
the future.


I have contacted n6bv and he reports they have already changed the 20th
edition of the Antenna Book back to the 'conventional' rho and changed the
power analysis to use the full hyperbolic formlations for voltage or current
to calculate the line loss.

Reflection-cooefficient bridges have been around for the last ONE HUNDRED &
FIFTY YEARS.

They have always incorporated artificial lines, or line simulators, or real
lines in the standard or reference arm of the bridge.

The reflection-coefficient bridge was used to locate faults on the first
oceanic telegraph cables by comparing the faulty cable with an artificial
version maintained at the terminal station specially for the purpose. An
artificial fault was moved along the artificial cable until the bridge was
balanced. The wideband signal generator was a 100-volt wet battery and a
telegraph key. The bridge unbalance indicator was a mirror galvanometer
using a light beam 5 or 6 feet in length and a sensitivity measured in
nano-amps.

The equipment was mounted on a mahogany bench, housed in beautifully
polished mahogany cases. Electrical connections were made by copper bars
between brass screw terminals, all changes in direction of bars were at
90-degrees. All brass and copper surfaces not needed for electrical
connections were brightly polished and coated with a clear laquer. The
overall appearance of the test room was a work of art, produced by a master
of his electrical and mechanical skills, with a quiet pride in the knowledge
that no-one else could possibly better improve operating efficiency of the
station and the cables which radiated from it in various directions under
the
ever-restless waves.

The same arrangement was used to locate oceanic cable faults in the 1970's.
I designed a fault locating test equipment with 10:1 bridge ratio arms which
saved space in the artificial line rack. The artificial line matched the
real
line from 1/10th Hz to 50 Hz. Cables had amplifiers every 20 or 30 miles
which also had to be simulated in the articial line.

For a 100 years or more, new multipair phone and other cable types have been
acceptance tested with reflection-coefficient bridges. One pair in the cable
is exhaustively tested for everything the test engineer can think of to make
sure there's nothing wrong with it. The known good pair is then used as the
standard arm of the bridge and each of the other 1023 pairs in the cable is
compared with it in the other arm of the bridge. It is a very sensitive
method of detecting cable faults. Care must be taken to terminate each pair
with its Zo. If standing waves are present then a dry high-resistance
faulty soldered joint might not be detected if it is located at a current
minimum.

Pulse-echo cable-fault locating test sets use a network to simulate the very
wideband line input impedance Ro + jXo. It is essential to balance-out in a
bridge the high amplitude transmitted pulse which would otherwise paralyse
the echo receiver

And for many years amateurs have unknowingly used reflection-coefficient
bridges immediately at the output of their transmitters. They have been
incorrectly named by get-rich-quick salesmen as SWR, forward and reflected
power meters. These quantities exist only in the users' imaginations and the
meter doesn't actually measure any of them.

A more appropriate name for the instrument is a TLI. (Transmitter Loading
Indicator). A pair of red and green LEDs would suffice to answer the
question " Is the load on the transmitter near enough to 50 ohms resistive
or is it not near to 50 ohms resistive ? "
---
Reg, G4FGQ

==========================================

"Peter O. Brackett" wrote
Reg:
[snip]
The fixed standard arm of the rho bridge (instead of a 50-ohms resistor)
can
be just a very long length of transmission line of input impedance Zo =
Ro+jXo which, of course, varies with frequency in exactly the required
manner.

Or, as I often did 50 years back, make an artificial lumped-LCR line
simulating network to any required degree of accuracy.
----
Reg
[snip]

Caution... take care, the "reflection police" may get ya!

Roy and Dave took me to task on another thread for even suggesting just
such
an
approach. A semi-infinite line!!! Hmph... no way they were gonna let me
get away
with that. Roy wanted to know what "semi-infinite" was!!!

Dave even told me that my idea of having a lumped approximation to Zo was
impossible!
This was a completd surprise to me since over 300,000 units of an xDSL
transceiver I
recently designed for the commercial marketplace and which have all been
shipped
and installed by BellSouth, Verizon, SBC and other such unknowing folks
incorporates
just exactly that kind of circuitre!

Hmmmm... I guess I lucked out and none of those customers noticed I was
balancing \
a lumped approximation of Zo against a real distributed complex Zo!

:-)

--
Peter K1PO
Indialantic By-the-Sea, FL.